Demodulating modulated signals with artificial neural networks

ABSTRACT

Demodulating a modulated signal. A method may include receiving a modulated signal, wherein the modulated signal is a signal modulated according to a modulation function varying faster than the signal. The modulation function is a function of the signal. The modulated signal received is demodulated with an artificial neural network system, or ANN system, which is trained to identify bit values from signal patterns as caused by the modulation function, by identifying bit values from patterns of the modulated signal received. Related modulation and demodulation systems are disclosed.

BACKGROUND

The present disclosure relates in general to techniques of demodulationusing artificial neural networks, and in particular to techniquesrelying on photonic computing systems configured as optical reservoirnetworks.

Machine learning mostly relies on artificial neural networks (ANNs),which are computational models inspired by biological neural networks inhuman or animal brains. Such systems progressively and autonomouslylearn tasks by means of examples; they have successfully been appliedto, e.g., speech recognition, text processing and computer vision.

An ANN comprises a set of connected units or nodes, which compare tobiological neurons in animal brains and are therefore called artificialneurons. Signals are transmitted along connections (also called edges)between artificial neurons, similarly to synapses. That is, anartificial neuron that receives a signal processes it and then signalsconnected neurons. In implementations, the signals conveyed along suchconnections are analog real numbers and outputs of the artificialneurons are computed thanks to a non-linear function of the sum of itsinputs. In photonic networks, signals can also be conveyed as complexnumbers.

Connection weights (also called synaptic weights) are normallyassociated with the connections and nodes; such weights adjust aslearning proceeds. Each neuron may have several inputs and a connectionweight is attributed to each input (the weight of that specificconnection). Such connection weights are learned by the trainingalgorithm during a training phase and thereby updated. The learningprocess is iterative: data cases are presented to the network, typicallyone at a time, and the weights associated with the input values areadjusted at each time step.

Many types of neural networks are known, starting with feedforwardneural networks, such as multilayer perceptrons, deep neural networksand convolutional neural networks. Besides, new types of neural networksemerge, such as spiking neural networks. A spiking neural network (SNN)substantially differs from usual neural networks, inasmuch as SNNsoperate using spikes, which may for example be discrete binary eventsthat can occur asynchronously at any point in time, rather than analogvalues computed at regular time-steps. That is, in addition to neuronaland synaptic state, SNNs further incorporate the concept of time. I.e.,neurons fire only when a membrane potential reaches a specific value,rather than firing at each propagation cycle as in, e.g., multi-layerperceptron networks. Firing means, in the context of SNNs, that a neurongenerates a signal that reaches other neurons, which, in turn, increaseor decrease their potentials according to the signals they receive fromother neurons.

Closely related, reservoir computing systems allow the analysis ofdynamical input data by training the output for certain tasks, e.g. forclassification or forecast purposes. Typically, inputs are fed into afixed, random dynamical system (the reservoir) and dynamics of thereservoir map inputs onto higher dimensional system. A suitably trainedreadout mechanism is then used to read the state of the reservoir, inorder to map this state onto the output, whereby only the readout stageneed be trained, while the reservoir is fixed. Main types of reservoircomputing include echo state networks and liquid-state machines (whichcan be regarded as a particular kind of SNN).

Neural networks are typically implemented in software. However, a neuralnetwork may also be implemented in hardware, e.g., as a resistiveprocessing unit or an optical neuromorphic system. For example, opticalcomputing systems (also called photonic computing systems) are known,which rely on photons (e.g., produced by light sources such as lasers ordiodes) for computation. For instance, application-specific devices suchas and optical correlators have been proposed, which rely on opticalcomputing to detect and/or track objects, or to classify serialtime-domain optical data.

SUMMARY

According to a first aspect, the present invention is embodied as amethod of demodulating a modulated signal. In one aspect, the methodcomprises receiving a modulated signal, wherein the modulated signal isa signal modulated according to a modulation function varying fasterthan the signal (i.e., in the time domain). The modulation function is afunction of the signal. That is, the signal can be regarded as avariable (i.e., the argument or input) of the modulation function. Themodulated signal received is demodulated with an artificial neuralnetwork system, or ANN system, which is trained to identify bit valuesfrom signal patterns as caused by the modulation function, byidentifying bit values from patterns of the modulated signal received.

The present approach makes it possible to decode the signal received(e.g., directly on the stream received) at a rate that is higher thanthe bit rate of the bit sequence captured by the signal. Because thespeed rate used is unknown to an attacker, this makes it virtuallyimpossible to reconstruct the bit-sequence without a properly trainedsystem. Now, beyond the fact that the encoding rate and the initial bitrate are unknown to an attacker, the resolution of the encoded signalmay fall under the temporal resolution of the physical detection deviceused by the attacker, making it impossible to detect for that device.

In embodiments, the method further comprises, prior to receiving themodulated signal: modulating the signal according to said modulationfunction to obtain said modulated signal; and transmitting the modulatedsignal obtained, for it to be received and subsequently demodulated bythe ANN system.

In some embodiments, the signal to be modulated is a digital signal;this signal is modulated over each time period corresponding to each ofthe discrete values captured by the digital signal, respectively, toobtain the modulated signal. The modulated signal can accordingly showvariations (or oscillations) within the time interval corresponding toeach discrete value of the initial signal, such that the resultingmodulation pattern varies faster than the underlying bit sequence (theraw bit rate) and, this, for each time period corresponding to eachdiscrete value of the initial digital signal.

In some embodiments, the modulation comprises, for each of said discretevalues, modulating said digital signal according to said modulationfunction based on two or more discrete values of the digital signal, thediscrete values including said each of the discrete values, as well asone or more previous discrete values of the digital signal.

In some embodiments, modulating the digital signal comprises streamingthe digital signal to a modulator, for it to modulate the signalstreamed on the fly, and transmitting comprises streaming the modulatedsignal to the ANN system for it to demodulate the streamed signal itreceives on the fly. In variants, the demodulation is done in astreaming mode, while the modulation is done in a buffered way.

In embodiments, the method further comprises converting the modulatedsignal received into a discrete signal, for the ANN system to demodulatethe converted signal by identifying bit values from patterns of valuesin the converted signal.

In some embodiments, the modulated signal is optically transmitted.

In some embodiments, the modulated signal received is an optical signaland the ANN system forms part of a photonic computing system, configuredas a reservoir computing system. In that case, the method may furthercomprise coupling the modulated signal received into the ANN for thelatter to demodulate the coupled signal by identifying bit values frompatterns of the coupled signal.

In some embodiments, the signal is modulated with an electro-opticmodulator, prior to being optically transmitted, for the transmittedsignal to be received and subsequently demodulated by the photoniccomputing system.

In embodiments, modulating the signal comprises modulating an amplitudeand/or a phase of an electromagnetic field carrying the signal.

In embodiments, modulating comprises modulating two or more inputsignals according to the modulation function, so as to obtain one ormore modulated signals, each varying faster than the input signals, themodulation function being a function of the input signals, such that oneor more modulated signals are subsequently received. I.e., the modulatedsignals are received (at the receiver) after modulation but such signalscould for instance be modulated in parallel and, therefore, received inparallel when using multiple parallel transmission channels. Invariants, however, the modulated signals may be transmitted one afterthe other. In all cases, the one or more modulated signals received aredemodulated (e.g., upon or after reception thereof) with the ANN system,by identifying bit values from patterns of the one or more modulatedsignals received.

In some embodiments, the ANN system is implemented as a trainablehardware device and the method further comprises, prior to demodulatingthe modulated signal received, mapping temporal information captured bythe modulated signal received onto one or more input nodes of an inputlayer of the ANN system. The ANN system further comprises an outputlayer of one or more output nodes. The input nodes of the input layerare connected to output nodes of the output layer via connections. Atleast some of these connections are associated to adjustable weightelements. In order to demodulate the modulated signal and therebyidentify bit values, the ANN system reads signals from said outputnodes.

The modulated signal may for instance be received as an optical inputsignal. In such cases, the ANN system may be implemented as part of aphotonic computing system configured as a reservoir computing system,whereby mapping said temporal information comprises coupling saidoptical input signal onto an input node of the reservoir computingsystem. The input node is connected to one or more optical output nodesof the output layer via optical reservoir nodes of a reservoir layer ofthe reservoir computing system. Each of said optical output nodes isconnected by one or more of the optical reservoir nodes via respectiveconnections. Adjustable weight elements are respectively associated tosaid respective connections.

In embodiments, said signal encodes, prior to modulating it, a n-arycode, with n larger than or equal to two, and the modulated signalencodes, after modulating it, a m-ary code, with m strictly larger thann.

In some embodiments, the method further comprises training the ANNsystem, for it to identify bit values from signal patterns as caused bythe modulation function.

In some embodiments, the method further comprises, after demodulatingthe modulated signal, adapting the modulation function based on feedbackobtained from the demodulated signal, so as to adapt a property of anext modulated signal, and modulating a subsequent signal based on theadapted modulation function.

According to another aspect, the invention is embodied as a demodulatorfor demodulating a signal. The demodulator notably comprises an inputunit configured to receive a modulated signal that is a signal modulatedaccording to a modulation function varying faster than the signal, themodulation function being a function of the signal. The demodulatorfurther comprises an ANN system connected to the input unit for thelatter to couple the received signal into the ANN system, in operation.Consistently with the present methods, the ANN system is assumed to betrained to identify bit values from signal patterns as caused by themodulation function; the ANN system is configured to demodulate themodulated signal coupled into it by identifying bit values from patternsof the modulated signal it receives, in operation.

In embodiments, the ANN system is a photonic computing system configuredas a reservoir computing system, the latter adapted to demodulate amodulated optical signal by identifying bit values from patterns of themodulated optical signal received by the input unit and coupled into theANN system, in operation.

In some embodiments, the ANN system is implemented as a trainablehardware device in the demodulator. The ANN system comprises an inputlayer of one or more input nodes and an output layer of one or moreoutput nodes, wherein the input nodes are connected to the output nodesvia connections and at least some of these connections are associated toadjustable weight elements. The ANN system is otherwise configured toidentify bit values by reading signals from said output nodes.

In some embodiments, the ANN system is implemented as a photoniccomputing system configured as a reservoir computing system, whichcomprises a single input node connected to one or more optical outputnodes of the output layer via optical reservoir nodes of a reservoirlayer thereof. Each optical output node is connected by one or more ofthe optical reservoir nodes via respective connections. Adjustableweight elements are respectively associated to said respectiveconnections. Finally, the input unit is configured to receive saidmodulated signal as an optical input signal and couple the latter intothe single input node.

According to a further and final aspect, the invention is embodied as amodulation system for modulating and demodulating a signal. This systemfirst comprises a modulator configured to modulate a signal according toa modulation function to obtain a modulated signal. Again, themodulation function is a function of the signal, which varies fasterthan the initial signal. The system further includes a transmission unitoperatively connected to the modulator to transmit modulated signalobtained by the latter, and a demodulator such as described above,wherein the input unit is configured to receive a modulated signaltransmitted by the transmission unit, in operation.

In embodiments, the signal to be modulated is assumed to be a digitalsignal and the modulator is configured to modulate the digital signalover each time period corresponding to each of the discrete valuescaptured by the digital signal, respectively, to obtain the modulatedsignal.

In some embodiments, the modulator is further configured to modulate,for each of said discrete values, said digital signal according to saidmodulation function, based on two or more discrete values of the digitalsignal, the discrete values including said each of said discrete values,as well as one or more previous discrete values of the digital signal.

In some embodiments, the modulator is adapted to modulate a streamedsignal on the fly, and the ANN system is further configured todemodulate a modulated signal it receives on the fly.

In some embodiments, each of the modulator and the ANN system is aphotonic computing system.

Apparatuses, computerized systems and methods embodying the presentinvention will now be described, by way of non-limiting examples, and inreference to the accompanying drawings.

BRIEF DESCRIPTION OF SEVERAL VIEWS OF THE DRAWINGS

The accompanying figures, where like reference numerals refer toidentical or functionally similar elements throughout the separateviews, and which together with the detailed description below areincorporated in and form part of the present specification, serve tofurther illustrate various embodiments and to explain various principlesand advantages all in accordance with the present disclosure, in which:

FIG. 1 is a diagram illustrating high-level steps of a method ofmodulating and demodulating signals, according to embodiments;

FIGS. 2A-2D and 3A-3D are plots of examples of signals (or portionsthereof) as involved in embodiments. Such signals are represented in thetime domain; the chosen examples are purposely simple. FIG. 2A shows anexample of a discrete signal, representing a sequence of values {1, 0,1, 0, 0, 1} as used in input for modulation. FIG. 2B illustrates anexample of synthesis signal, as obtained after modulating the inputsignal of FIG. 2A with a modulation function, wherein the modulationfunction produces signal pulses as depicted in FIGS. 3A and 3C, based ona current (instantaneous) values (0 or 1) of the discrete input signal.FIGS. 3B and 3D are discrete counterparts of the analog signal pulses ofFIGS. 3A and 3C. Whereas the signal obtained in FIG. 2B is an analogsignal, FIGS. 2C and 2D show examples of discrete modulated signalsobtained by modulating the initial sequence of FIG. 2A based on moresophisticated substitution schemes, where the modulation function takesprevious values of the signal as arguments, in addition to aninstantaneous value;

FIG. 4 schematically depicts an optical reservoir network, as well asselected components of a photonic computing system configured toimplement such a network, as involved in embodiments;

FIG. 5 schematically illustrates selected components of another photoniccomputing system, also configured as an optical reservoir, as involvedin other embodiments; and

FIG. 6 is a flowchart illustrating high-level steps of a method ofmodulating and demodulating a signal, according to embodiments.

The accompanying drawings show simplified representations of apparatusesand systems, or parts thereof, as involved in embodiments. Technicalfeatures depicted in FIG. 5 are not to scale. Similar or functionallysimilar elements in the figures have been allocated the same numeralreferences, unless otherwise indicated.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

Neural cryptography relies on stochastic algorithms (e.g., ANNalgorithms) for use in encryption and cryptanalysis. One may indeedcontemplate using neural networks to handle encrypted data, since ANNsmay, in principle, reproduce any function. I.e., a suitably trained ANNmay possibly be used to find an inverse-function of a cryptographicalgorithm. Although no practical applications have been proposed todate, one understands that encrypted data are at risk, owing to therapid development of ANNs.

Based on this observation, the present Inventors came up with aconceptually simple solution to improve the security of encrypted, whichmay advantageously exploit a hardware-based encryption/decryptiontechnology. This is explained in detail in the following description,which is structured as follows. First, general embodiments andhigh-level variants are described (sect. 1). The next section addressesmore specific embodiments and technical implementation details (sect.2).

1. General Embodiments and High-Level Variants

In reference to FIGS. 1 and 6, an aspect of the invention is firstdescribed, which concerns a method of demodulating a modulated signal,i.e., a method as implemented on the receiver side 20.

In some embodiments, this method relies on a modulated signal 54, whichis received at step S12, wherein the modulated signal 54 is assumed tohave been obtained by modulating (11, step S11) a given signal 51. Morespecifically, this signal 54 has been modulated thanks to a modulationfunction 52 that varies faster than the initial signal 51 (in the timedomain). The modulation function 52 is a function of the signal 51: ittakes the initial signal 51, values thereof, or values captured thereinas arguments in order to produces a modulated signal 53. Such a signal53 can then be transmitted S12 (as a signal 54) and coupled S21 as asignal 55 into an artificial neural network system 22 (hereafter ANNsystem) 22 for demodulation purposes.

That is, the modulated signal 55 is demodulated S22 using the ANN system22, e.g., a trainable hardware device or computer system. Moreprecisely, the system 22 is trained to identify bit values from signalpatterns as caused by the modulation function 52, in operation. Thedemodulation S22 is carried out by identifying bit values from patternsof the modulated signal 54 received.

Comments are in order. In the present context, themodulation/demodulation operations performed amounts to encoding (orencrypting)/decoding (decrypting) data or signal values faster than theinitial signal does. The demodulation may for instance be operateddirectly on the signal itself (amplitude, phase, etc.) or on discretevalues it represents, as exemplified later.

The signal 51 as initially considered (prior to modulating S11 it) mayfor instance be a digital signal (e.g., as output by a digital circuit)or an analog signal (e.g., as output by a sensor or an analog circuit).A digital signal can for example be a pulse train (a pulse amplitudemodulated signal) or a physical signal that is sampled and quantized. Adigital signal may thus convey a discrete signal (or discrete-timesignal), as a time series of values. In all cases, the time-varyingquantity is, in a digital signal, a representation of a sequence ofdiscrete values (a finite number of values). A digital signal is thusoften referred to as a discrete signal. On the contrary, an analogsignal is continuous in time, e.g., a sinus-shaped signal with a certainamplitude modulation or phase modulation, where the time-varyingquantity is a representation of another time-varying quantity. Be itanalog or digital, the initial signal 51 captures information to betransmitted. Such information may be captured as two or more bit values,for example.

This initial signal 51 is assumed to have been modulated S11 accordingto a modulation function ƒ(·). This function may be a digital modulationfunction, producing discrete signals (as exemplified in FIGS. 3B, 3D) orcontinuous signals in output (as in FIGS. 3A, 3C). In all cases, thesignal 53 resulting from the modulation step S11 may be a digital or ananalog signal, and may be conveyed S12 (i.e., transmitted) electricallyor optically, for example. Still, the intermediate transmission step S12could use any wave transmission technology, such as acoustic waves, forexample. The changes in the resulting carrier signal caused by themodulation S11 may for example form a finite (but typically large)number of alternative symbols making up a modulation alphabet, as inembodiments discussed below.

Consistently, the modulated signal 54 received at step S12 may bereceived in the form of a digital or an analog signal. It may forexample be initially received S12 in the form of an analog signal, whichmay then possibly be converted S21 into a digital signal, e.g., sampledand interpreted as a set of successive discrete values, for subsequentdemodulation purposes S22. In this case, the ANN system 22 demodulatesS22 the converted signal by identifying S22 bit values from patterns ofvalues in the converted signal. That is, the identification S22 operatesbased on discrete values rather than signal's characteristics. Yet, thedemodulation step S22 need not necessarily be performed on discretevalues and may instead be performed on the modulated signal itself, asnoted above. I.e., the identification step S22 may be performed based onthe signal's characteristics, for example based on an optical signal.For example, the modulated signal may well be transmitted optically andthen optically coupled into the ANN system 22, the latter configured asan optical reservoir, as in embodiments discussed later.

Note, fiber optic data transmissions typically use square waves and theunderlying signal is normally considered as a digital signal. However,in the present case, the signal conveyed depends on the initial signal51 used and the modulation function 52, such that the fiber optic signalmay not be a square wave anymore.

When using a software implementation of the ANN 22, the demodulationstep S22 directly leads to a set of digits, e.g., {1, 0, 1, 0, 0, 1},corresponding to digits captured by the initial signal 51. In variantsrelying on hardware implementations of the ANN 22 (i.e., where the ANNis a special-purpose hardware device, rather than a computer configuredto implement an ANN), the demodulation step S21 shall typically lead toan intermediate signal (not shown), from which the final sequence isretrieved, as assumed in FIG. 1. When using a hardware optical network22, for example, the signal obtained in output of the ANN 22 maytypically be a stream of optical power (light of varying intensity),whose variations capture the same values as the initial signal 51. Thus,the signal obtained in output from step S22 may again be a discrete oranalog signal, yet capturing values corresponding to those of theinitial signal 51. Note, in embodiments, multi-level signals may be usedin place of a binary signal, notwithstanding depictions used in FIG. 1.

The demodulation step S22 may be regarded as a classification ofpatterns formed by the signal 54 received S12 and then 55 coupled S21into the ANN 22, wherein the classification is carried out by means ofthe ANN system 22. The ANN system 22 is assumed to be trained toidentify bit values from patterns caused by the modulation function 52,i.e., patterns of values or corresponding signal patterns produced bythis function 52, in operation. Thus, at inference time, the system 22allows bit values to be identified S22 from patterns of the modulatedsignal 55, be it directly (as in software implementations of the ANN) ornot (as in implementations using special-purpose ANN hardware).

If needed, the signal 54 received at step S12 may first be converted S21into digital values for the system 22 to suitably classify patternsformed in such digital values, i.e., values which are anyway representedor captured by the signal 54. In one aspect, however, the ANN systemdirectly operates S22 on the signal 54 as received. In such cases, thesignal 55 coupled into the ANN 22 is “identical” to the signal 54received at step 54 (subject to the coupling step S21, which mightimpact properties of the signal 54), such that no analog-to-digitalconversion is needed in that case, making the demodulation S22 moreefficient. Note, coupling the signal into a hardware ANN, for example,might impact the signal, e.g., cause optical losses and thus result in asmaller amplitude. Thus, the coupled signal will typically not beperfectly identical to the signal 54 in that case.

The present approach makes it possible to decode the signal received(e.g., directly on the stream received) at a rate that is higher thanthe bit rate of the bit sequence captured by the signal 51, thanks tothe fact that outputs from the modulation function vary faster than theinitial signal, as explained below. Because the resulting modulationspeed used is unknown to an attacker, this makes it virtually impossibleto reconstruct the bit-sequence without a properly trained system. Now,beyond the fact that the encoding rate and the initial bit rate areunknown to an attacker, the temporal resolution of the encoded signal 54may fall under the resolution of the physical detection device used bythe attacker, making it impossible to detect for that device. Forexample, using a hardware-implemented ANN makes it possible to operateat much higher frequencies than a typical physical detection device.E.g., such an ANN converts a “high-speed” encrypted signal into a“low-speed” decrypted signal

That the modulation function varies faster than the initial signalbasically means that the derivative of the modulated signal will, onaverage, change sign more often than the derivative of the initialsignal (or a quantity captured by the latter) over a same time period.Such conclusions apply to continuous and differentiable signals and mayhold for higher-order (n-th) derivatives, for signals of class C^(n).For discrete/sampled signals, that the modulation function varies fastermeans that the successive differences of the modulated signal values ofthe modulated signal will, on average, change sign more often than thesuccessive differences of the initial signal (or a quantity captured bythe latter) over a same time period. Such differences are computed overintervals corresponding to the smallest temporal resolution available.Similar conclusions hold for the n-th differences (n>1). I.e., outputsfrom the modulation function oscillate faster in the time domain. Thiswill typically result in that the modulated signal has a temporalfrequency (i.e., a characteristic frequency or frequencies) that, onaverage, is higher than the temporal frequency (or characteristicfrequencies) of the initial signal 51. I.e., the corresponding Fourierspectrum shifts to larger frequencies after modulation and theautocorrelation function falls off more rapidly from its maximum at lag0, over the time interval corresponding to a minimal modulation timeperiod of the modulation function.

For discrete signals, the modulation function can be said to have asmaller temporal resolution than the initial signal. For example, thesignal shown in FIG. 2C shows eight pulses, where the signal of FIG. 2Ahas three over the same time interval. The higher temporal frequency ofthe modulated signal may be characterized by usual techniques in signalanalysis and processing, e.g., via Fourier analysis, using power spectraof the signals, etc. Note, the above considerations pertain to theuseful parts of the initial and modulated signals, once noise has beenfiltered out, if necessary. Yet, and notwithstanding possible noise, itremains the modulated signal will, for its essential (and useful) part,vary faster than the initial signal, for its essential (and useful)part.

As evoked above, the ANN system 22 is a cognitive system, which maypossibly be implemented in software or, in hardware (as aspecial-purpose ANN hardware). The cognitive system may for instance beimplemented as any suitable machine learning model, i.e., implemented insoftware run on a classical computer platform. It may notably beimplemented as a spiking neural network or an auto-encoder, for example.Yet, such a computer platform may nevertheless integrate dedicatedaccelerators and other hardware optimizations for ANN. Similarly,co-optimized software and hardware platforms may be relied on. Still,the ANN system can be implemented in special-purpose ANN hardware, i.e.,as a trainable hardware device such as a photonic computing systemconfigured as an optical reservoir or a resistive processing unit, forthe sake of speed upon demodulating and security forcrypto-applications. In particular, it may advantageously be implementedas an optical reservoir hardware system, to enable high-speed decodingand crypto-applications compatible with high raw bit rates, based onoptical signals, as discussed later in detail.

Note that, in the literature, the terms cognitive algorithm, cognitivemodel, machine learning model or the like are interchangeably used. Inan effort to clarify terminologies, one may tentatively adopt thefollowing definition: a machine learning model is generated by acognitive algorithm, which learns its parameters from input data points,so as to arrive at a trained model. Thus, a distinction can be madebetween the cognitive algorithm being trained and the model thateventually results called trained model upon completion of the trainingof the underlying algorithm. Similarly, a distinction can be madebetween a trainable special-purpose ANN hardware and a trained hardwaredevice. The special-purpose hardware device 22 as used in someembodiments for demodulation purposes S22 are assumed to have alreadybeen suitably trained with respect to the modulation function 52 asinitially used to modulate S11 the signal 51.

All this is now described in detail, in respect of particularembodiments of the invention.

The method and variants described so far primarily revolve around thedecoding/demodulation step S22 performed at the receiver 20. However,the present invention extends to methods implemented both at thetransmitter side 10 and receiver side 20. Thus, in embodiments, thepresent methods also include modulating S11 the initial signal 51according to the modulation function 52, in order to obtain a modulatedsignal 53. The modulated signal 53 obtained is then transmitted S12, forit to be received S12 and subsequently demodulated S22 by the ANN system22.

The initial modulation S11 may for instance be achieved by digitalsignal processing (DSP), where digital modulation is sought. Themodulated signal 53 obtained S11 can then be transmitted S12electrically or optically, as evoked earlier. In variants, use can bemade of an electro-optic modulator (EOM), in order to modulate S11 abeam of light, which can then be transmitted optically. E.g., a digitalsignal 51 may first be digitally processed and then optically encoded.To that aim, fast EOMs can be relied upon, such as lithium niobate orsilicon-based EOMs, which devices are known per se. In other variants,the initial (digital or analog) signal 51 may be subjected to analogsignal processing S11. Assume, for example, that the initial signal 51is a digital signal, as in FIG. 1 (see also FIG. 2A). Since, for thepresent purposes, the modulation function 52 needs to vary faster thanthe input signal, the initial signal 51 may for instance be modulatedS11 over each time period corresponding to each of the discrete valuescaptured by the digital signal 51, respectively, to obtain the modulatedsignal 53. FIGS. 2B-2D show possible examples of resulting signals 53.For example, the modulation S11 may be based on instantaneous values ofthe discrete signal 51, where the initial bit sequence 51 is streamedthrough the modulator 11. As in amplitude modulation, an instantaneousvalue refers to the value as currently taken into account by thefunction 52 of the modulator 11, denoted by f(·) in FIG. 1. That is, themodulation function 52 may, based on a current value of the discretesignal and for each current value that is successively processes,produce a signal pulse (as in FIG. 2B) or a digital signal representinga set of several, distinct values (as in FIGS. 2C, 2D). As seen in FIGS.2B-2D, the modulated signal varies “faster” than the input signal. I.e.,in each case, the modulated signal shows several variations(oscillations) within the time interval corresponding to each discretevalue of the initial signal of FIG. 2A. All such time intervals arenormally constant, such that the resulting modulation pattern variesfaster than the underlying bit sequence (the raw bit rate) and, this,for each time period corresponding to each discrete value of the initialsignal 51. Note, while the time period over which the initial signalvaries is 1 (a.u.) in FIG. 2A, the basic time period over which signalsof FIGS. 2C and 2D are modulated is ¼ (a.u.).

FIGS. 3A and 3C show two different pieces of continuous (analog) signalsproduced by a given modulation function for transforming a “1” and a“0”. Applying this function to the initial sequence of FIG. 2A modulatesthis sequence and yields a signal as shown in FIG. 2B, which interleavespatterns according to FIGS. 3A and 3C. Because FIGS. 3A and 3C involveanalog-like transformations, the signal obtained in FIG. 2B can beregarded as an analog signal.

On the contrary, applying a discrete modulation function to the initialsequence of FIG. 2A would result in a discrete signal. For example,FIGS. 3B and 3D are discrete counterparts of the analog pieces of FIGS.3A and 3C, which could be used to modulate the input signal of FIG. 2A.The outcome of such a modulation is not shown.

Yet, one understands that the initial signal 51 may possibly be adiscrete signal, modulated by a discrete or analog modulation function,or an analog signal, which is, e.g., sampled for modulation purposes bya discrete modulation function. In variants, an analog modulation may beused to modulate the initial, analog signal, e.g., based on theinstantaneous value of the analog input signal read (as in frequencymodulation). What matters for the present purpose is that the modulationfunction varies faster than the initial signal (or the quantityrepresented by the latter).

Instead, FIGS. 2C and 2D depict modulated signals obtained by modulatingthe initial sequence of FIG. 2A according to more sophisticatedsubstitution schemes, wherein previous values of the initial signal aretaken into account, in addition to its instantaneous value. Namely, FIG.2C is obtained by modulating the initial sequence FIG. 2A according to asubstitution {k, l}→{p, q, r, s}, while FIG. 2D is obtained bymodulating the same initial sequence according to the substitution {k,l}→{p, q, r}, yielding distinct time step subdivisions. While themodulation performed in FIG. 2C remains of binary form, the modulationin FIG. 2D yields a ternary code (a multi-level signal). Suchsubstitution rules are described below detail.

First, we note that the modulation step S11 may advantageously operateon operands constituted by several discrete values of the initial signal51. That is, each discrete value of the signal 51 may be modulatedaccording to a modulation function 52 that takes two or more discretevalues of the signal 51 in input. E.g., for each current value of theinitial signal 51, the function ƒ may take the current value as well asone or more previous discrete values of the signal as input, to producea modulation, as assumed in FIGS. 2C and 2D. I.e., the initial bitsequence {1, 0, 1, 0, 0, 1} is modulated according to a parametricmodulation.

In the example of FIG. 2C, the modulation function is assumed to performsubstitutions as listed below: {k, l} again denotes an input pair ofvalues, where l is a current (instantaneous) value and k the valueimmediately preceding the current value l in the initial bit sequence,whereas the sets {p, q, r, s} denotes modulated sets as produced inoutput:

{0, 0}→{0, 0, 1, 1}

{0, 1}→{0, 1, 1, 0}

{1, 0}→{1, 0, 0, 1}

{1, 1}→{1, 1, 1, 0}

That is, the basic time period is divided by two in this example(compare FIGS. 2C and 2A). Note, such substitutions will typicallyrequire to properly initialize the initial sequence, in order to enablea substitution for the very first or very last bit in the initialsequence. A dummy bit (e.g., 0) may for instance be prepended to theactual initial sequence. E.g., the initial sequence {1, 0, 1, 0, 0, 1}shown in FIG. 2A may first be interpreted as the modified sequence {{0},1, 0, 1, 0, 0, 1}, where {0} is prepended to {1, 0, 1, 0, 0, 1}. Then,the first actual value of the sequence {1, 0, 1, 0, 0, 1} of FIG. 2A,which is 1, gives rise to an input pair value {0, 1}, consistently withthe modified sequence. This, in turn, gives rise to the modulation {0,1, 1, 0}, operated on a time step that is twice smaller than theinitial's. The second actual value of the initial sequence of FIG. 2A is0, which gives rise to the input pair {1, 0}, since the immediatelypreceding value is 1. This, in turn, leads to a modulated set {1, 0, 0,1}, according to the above substitution list, and so on. Eventually,this leads to the modulated pattern depicted in FIG. 2C. The dummy bitprepended to the initial sequence need eventually be removed from thediscrete signal 56, once reconstructed (after step S22). In variants,one may append a dummy bit, instead of prepending it to the initialsequence.

Note, where discrete signals are used, neither the initial signal 51 northe modulated signal 53 need necessarily be binary signals (representingvalues of 0 or 1). For example, the modulation function 52 may use aternary code to encode information, as assumed in FIG. 2D. Still, thearity of the modulated code can exceed that of the input code, to makeit more difficult for an attacker to decode a sequence. Thus, while theinitial signal 51 may encode a n-ary code (with n≥2), the modulatedsignal 53 can encode, after modulation S11, a m-ary code, with m>n. Thisis exemplified in FIG. 2D, where a ternary code is obtained aftermodulation S11, contrary to the binary encoding used in input (FIG. 2A).

More in detail, the following substitutions are assumed to be performedto obtain the signal of FIG. 2D, upon encoding S11. Again, a dummy bit(0) is assumed to have been prepended to the actual initial sequence. Inthe following list, {k, l} denotes an input pair of values, where l is acurrent value of the input signal, while k is a previous value of thegiven bit sequence, and {p, q, r} denotes modulated sets as produced inoutput of the modulation function 52:

{0, 0}→{0, 2, 1}

{0, 1}→{0, 1, 2}

{1, 0}→{1, 2, 0}

{1, 1}→{2, 1, 0}

Such substitutions give rise to the ternary sequence shown in FIG. 2D.

In variants to FIG. 2D (where the modulated signal encodes a m-ary codeafter modulation, with m>n.), the n-ary code may simply be convertedinto another n-ary code (i.e., m=n, based on a different temporal basis,as exemplified earlier in reference to FIG. 2C. In still other variants,the parity of the modulated signal may even be smaller than n (i.e.,m<n), provided that the frequency of the signal is further modulated tocompensate for the missing dimension. While the latter is easier to tap,it may nevertheless be more robust in transmission.

Note, the examples of modulations given in FIGS. 2B-2D are pedagogicalexamples: in practice, the modulations performed at step S22 shalltypically operate on much longer initial sequences {k, l, . . . } andproduce longer output sequences. In addition, the substitutions need notbe static and could instead evolve over time. Moreover, moresophisticated, dynamic encoding may take place. Thus, the primary ANNsystem 22 may possibly need be re-trained S30 over time, as assumed inthe flowchart of FIG. 6.

In simpler variants, however, each modulation step is based on a singlevalue of the digital signal, i.e., based on the instantaneous valuethereof, as assumed in FIG. 2A, where different bit values lead todistinct signal pulses (see FIGS. 3A, 3C) or discrete sequences (FIGS.3B, 3D). Correspondingly, the modulation S22 may possibly result in acontinuously varying signal (as in FIG. 2B) or a discrete signal (FIGS.2C, 2D). In all cases, it remains that the added complexity of thehigher frequency (or higher bit-rate) of the output signal (or sequence)makes it very difficult to interpret the signal 54, 55 without asuitably trained ANN and prior knowledge of the time step (bit rate) ofthe initial signal 51 and the modulation function 52.

In embodiments, the digital signal 51 is initially streamed S10 to amodulator 11, for it to modulate S11 the signal on the fly. Again,previous signal values may be used together with the instantaneoussignal value to perform the modulation S11, as exemplified above.Consistently, the modulated signal 54 may be streamed to the ANN system22 for it to demodulate S22 the streamed signal it receives on the fly.

In variants, the signal's values could possibly be re-arranged in blocksor arrays of block of sequences of bits, prior to modulating S11 there-arranged signals. Such sequences can then be modulated S11 one afterthe other or in parallel, and then similarly demodulated, beforere-assembling the sequence of values. In that respect, modulationpatterns may be learned S30 across several, parallel sets of modulatedsequences. Again, complex modulation schemes may be contemplated, toform complex symbols, notwithstanding the simple examples assumed inFIGS. 2-3.

An aspect is to modulate S11 two or more input signals in parallel(thanks to a modulation function 52 operating on all input signalsconsidered), to obtain one or more modulated signals 53. Again, theresulting modulated signal(s) will vary faster than the input signals.The one or more modulated signals 54 as subsequently received at stepS12 are then demodulated S22 with the ANN system 22 by patternrecognition, i.e., by identifying bit values from patterns of the one ormore modulated signals 54 received at step S12. The initial signals 51may for instance be input streams (i.e., sequences of data elements) ina software implementation of the ANN. In variants, it may be a set ofanalog signals. Thus, the modulation step S11 may result in a singlestream or a single modulated, analog signal, or several streams orsignals, which are fed S21 into the ANN for demodulation, so as torestore information comprised in the inputs signal(s).

The ANN may advantageously be a reservoir network. Now, for reasons ofboth efficiency and security, the ANN system 22 can be implemented as atrainable hardware device (i.e., a special-purpose ANN hardware), ratherthan in software. Also, and as evoked earlier, the modulated signal 54may notably be optically transmitted S12, whereby the signal 54 receivedat step S12 is an optical signal 54. In that case, one mayadvantageously use a photonic computing system 20 to perform thedemodulation S22. More precisely, the ANN system 22 may form part of aphotonic computing system 20, configured as a reservoir computingsystem. Coupling S21 the optical signal 54 received into the ANN 22causes the ANN 22 to demodulate S22 the coupled signal 55 by identifyingbit values from signal patterns in the coupled signal 55.

As said, the signal 51 may for instance be modulated S11 with an EOM 11,prior to being optically transmitted S12, for the transmitted signal 54to be received S12 and subsequently demodulated S22 by the photoniccomputing system 20. Still, while an EOM may advantageously be used tomodulate the signal, other solutions can be contemplated to achieve thesame. One such solution is to rely on a linear optical network withdelay lines working with coherent light, see, e.g.,https://arxiv.org/ftp/arxiv/papers/1501/1501.03024.pdf.

One may for instance rely on a linear optical network (withinterconnected delay lines) to encode information in both the amplitudeand the phase of the electromagnetic field carrying the signal. Invariants, the modulation S11 may be based on the sole light intensity(only the amplitude of the field is modulated) or the sole phase. Whilethe encoded signal 51 may be a digital signal, it may also be, in othervariants, a mere analog signal (e.g., electrical), as mentioned earlier.

Whether implemented as a trainable hardware device (i.e., aspecial-purpose ANN hardware) or in software, the basic workingprinciple of the ANN, however, remains the same, as discussed now inrespect of FIG. 4. First, temporal information captured by the modulatedsignal 54 need be mapped S21 onto one or more input nodes 251 of theinput layer of the ANN. The input nodes 251 of the input layer areconnected to one or more output nodes 254 of the output layer of the ANNvia connections. At least some of these connections are associated toadjustable weight elements, i.e., they can be adjusted during a trainingprocess, making the system 22 a trainable system. The identification ofbit values performed at step S22 requires to read signals from theoutput nodes.

Note, FIG. 4 assumes several input nodes and output nodes. In variants,however, each of the input and output layers may comprise a single node.In all cases, temporal information (and possibly additional information)contained in the signal 54 received at step S12 may first be adequatelymapped S21 onto input nodes 251. The output nodes 254 may possibly bemapped onto distinct bit values or analog values. The actual bit values56 are inferred thanks to the trained, weight elements 253, by suitablycombining and weighting the values read in output.

Note, a similar architecture may be implemented in software, e.g., byway of a spiking neural network, or SNN, wherein, for example, outputnodes are connected to each other via all-to-all lateral inhibitoryconnections, while input nodes are connected to output nodes viaall-to-all excitatory connections, to which connection weights areassociated. Other types of ANNs can be contemplated, such as FFNs, forexample.

As discussed earlier, the modulated signal 54 received at step S12 maybe an optical signal, in which case the ANN system 22 may advantageouslybe implemented as part of a photonic computing system 20, configured asa reservoir computing system. In that case, temporal information may bemapped S21 onto the reservoir computing system 22 by coupling theoptical signal 54 onto input nodes 251 thereof. As further seen in FIG.4, an input node 251 may be connected to one or more optical outputnodes 254 via optical reservoir nodes 252 of a reservoir layer of thesystem 22. Each of the optical output nodes 254 will typically beconnected by one or more of the optical reservoir nodes 252 viarespective connections, to which adjustable weight elements 253 arerespectively associated. Note, notwithstanding the depiction of thespecific implementation of the reservoir shown in FIG. 4, the nodes 252shall typically be connected in practice.

Reservoir computing systems allow an efficient analysis of dynamicalinput data by training the output. The ANN system may notably beimplemented as a liquid-state machine or an echo state network. Inembodiments, the reservoir layer may be achieved in the form of anoptical interference pattern having a given optical power distribution,as assumed in FIG. 5. This way, temporal information of the opticalinput signal can be mapped into the optical interference pattern. Also,the output connections and associated weight elements may operate in theoptical domain. The optical reservoir system shown in FIG. 5 is furtherdescribed in sect. 2.1.

As illustrated in FIG. 6, the present methods may further comprisetraining S30 the ANN system, for it to identify bit values from signalpatterns caused by the modulation function 52. This can notably beachieved by sending a training data set and then train S30 the ANN 22based on the dataset received. The ANN 22 may notably be retrained S30,as necessary, e.g., upon changing the modulation conditions or changingthe signal connection path. In security-sensitive applications, thetraining of the system 22 must be handled with care. The trainingdatasets may for instance be transmitted using another channel than thechannel used for inference purposes S22. Note, when using an opticalnetwork 22, changing the physical connection path might requirere-training the system 22, in particular when the phase of the signal ismodulated S11 and/or interpreted S22.

The modulation function 52 used at step S11 may need be adapted S50 forsecurity reasons or in order to adapt to a dynamically evolving context:different types of data as used at a certain point in time may require adifferent type of modulation. Moreover, the modulation function 52 maypossibly be updated S50 based on feedback received S40 from the ANNsystem 22, upon analyzing S40 properties of the demodulated signal S12,and so as to adapt a property of a subsequently modulated signal 51 (asignal modulated during a next cycle). This may notably be done so as tofulfill or optimize certain boundary conditions (e.g., maintain aconstant average value of the modulated signal), or in view of improvingthe signal transmission (e.g., reducing the transmission errors byselecting an optimal function 52, in order to improve the physicalcontrast between different input states after decoding or the encodingefficiency). Note, the property(ies) analyzed at step S40 refer(s) to asignal 55 as received at the receiver. Thus, the analysis performed atstep S40 impacts a next cycle S11-S22. For example, feedback receivedowing to step S40 may be used to ensure to maintain a constant averagevalue of the modulated signal throughout subsequent cycles. Note thatupdates of the modulation function 52 might occur immediately after eachcycle S11-S22, or after multiple cycles and multiple batches of trainingdata.

For example, a second trainable ANN (not shown) may be used for thesignal generation, upstream the modulator 11, so as to impact themodulation function 52. This second ANN can be used together with acontrol circuitry on the receiver side 20 to adjust the encodingfunction 52, so as to fulfill or optimize said boundary conditions, forexample.

Next, according to other aspects, the invention can be embodied as acomputing system, such as a demodulator 20 or a whole modulation system1. Aspects of such systems have already been implicitly addressed inreference to the present methods and are only succinctly described inthe following, in reference to FIGS. 1, 4 and 5.

First, the invention may be implemented as a sole demodulator 20 fordemodulating a signal according to methods described earlier. Such ademodulator 20 can comprise an input unit 21 and an ANN system 22. Theinput unit 21 is configured to receive a modulated signal 54, i.e., asignal modulated according to a modulation function 52, so as to varyfaster than the initial signal 51, as discussed earlier. The ANN systemis connected to the input unit 21 for the latter to couple the receivedsignal 54 into the ANN system 22, in operation. As explained earlier,the ANN system 22 is assumed to be trained to identify bit values fromsignal patterns caused by the modulation function 52. The system 22 isotherwise configured, in the demodulator 20, so as to demodulatemodulated signals 55 coupled into it by identifying bit values frompatterns of the modulated signal 54 received.

Referring to FIGS. 4 and 5, the ANN system 22 may notably be a reservoircomputing system, e.g., form part of a photonic computing system 20configured as a reservoir computing system. Such a reservoir computingsystem is adapted to demodulate an optical signal 53, 54 by identifyingbit values from patterns of the modulated optical signal 53 received bythe input unit 21 and then coupled into the ANN system 22, in operation.

As seen in FIG. 4, the ANN system may notably comprise an input layer ofone or more input nodes 251, as well as an output layer of one or moreoutput nodes 254. The input nodes 251 are connected to the output nodesvia connections (arrows), where at least some of these connections areassociated to adjustable weight elements 253. The ANN system 22 mayidentify bit values by reading signals from said output nodes 254, inoperation. More generally though, the ANN system 22 may be implementedas a trainable, special-purpose hardware device in the demodulator 20.

The input unit 21 may further be configured so as to map temporalinformation (and/or specific information, other dimensional information,such as wavelength, polarization, core in a multi-core fiber) capturedin the modulated signal 54 onto input nodes of the system 22. Invariants, the input unit 21 may simply couple (e.g., optically) thesignal 54 onto a single input node.

In the system 22 depicted in FIG. 4, the input nodes 251 are connectedto optical output nodes 254 via optical reservoir nodes 252 of areservoir layer of the system 22. Each optical output node 254 isconnected by one or more of the optical reservoir nodes 252 viarespective connections, to which adjustable weight elements 253 arerespectively associated. The input unit 21 is configured to receive amodulated signal 54 as an optical input signal 54 and couple the latterISi into the input nodes 251, as described in detail in sect. 2.1.

Another example of a photonic computing system 22 a is shown in FIG. 5,which is described in detail in sect. 2.1.

Note, in implementations relying on optical reservoir networks, thereceiver 20 may further comprise an optical detector, which, however,would be positioned downstream the ANN 22. In other words: the signal 54is first fed S21 into the optical ANN 22, and then detected with theoptical detector, the input unit 21 being basically a coupler in thatcase, meant to couple the received signal into the ANN.

In variants where a non-optical system such as a RPU is used, instead ofan optical reservoir, the input unit 21 should similarly be configured(e.g., programmed) to map temporal information (and possibly otherinformation, such as amplitude, phase, etc.) captured in the inputsignal onto various input nodes of the ANN, for them to relay thesignals into upper layers of the network.

Referring back to FIG. 1, according to another aspect, the invention canbe embodied as a modulation/demodulation system 1 for both modulatingand demodulating a signal. That is, such a system 1 comprises both ademodulator 20 (such as described earlier) and a modulator 11. Thelatter is configured to modulate a signal 51 according to a modulationfunction 52 to obtain a modulated signal. As explained earlier, themodulation function 52 is a function of the signal 51 (i.e., it takesthe signal 51 as an input) and its outputs vary faster than the signal51. Moreover, the system 1 includes a transmission unit operativelyconnected to the modulator 11, so as to transmit modulated signalsobtained by the latter.

Again, the modulator 11 may possibly be configured to modulate a digitalsignal 51, e.g., over each time period corresponding to each of thediscrete values captured by the digital signal 51, respectively, toobtain the modulated signal 53. In addition, the modulator 11 mayfurther be configured to modulate the digital signal 51 based on two ormore discrete values thereof (e.g., the instantaneous value, as well asone or more previous values), thanks to a suitable modulation function52. The modulator 11 may for instance be adapted to modulate a streamedsignal on the fly. Similarly, the ANN system 22 may possibly be designedto demodulate on the fly, in particular when using a special-purposeoptical system.

The above embodiments have been succinctly described in reference to theaccompanying drawings and may accommodate a number of variants. Severalcombinations of the above features may be contemplated. Examples aregiven in the next section.

2. Specific Embodiments—Technical Implementation Details

2.1 Optical Reservoir Computing Systems

FIG. 4 schematically depicts a photonic computing system 22 embodied asoptical reservoir computing system, according to embodiments. Thephotonic computing system 22 comprises an input layer, a reservoir layerand an output layer. The input layer comprises a plurality of inputnodes 251, configured so as to receive optical input signals ISi (e.g.,optical input streams) and forward such signals ISi to the reservoirlayer. The reservoir layer comprises a confined reservoir region, e.g.,a continuous optical reservoir region 410 with a plurality of opticalreservoir nodes 252. The reservoir layer is here formed as an opticalinterference pattern having an optical power distribution, as describedlater in reference to FIG. 5.

The photonic computing system 22 comprises further a plurality ofoptical output connections between the reservoir nodes 252 and theoutput nodes 254. At least some of the optical output connections areassociated to weighting elements (wi) 253, which can be adjusted duringthe training process S30. I.e., the optical reservoir system 22 can betrained to perform specific computation tasks as discussed in sect. 1.

In an optical reservoir system such as depicted in FIG. 4, the inputnodes 251 may be embodied as optical input waveguides, e.g., as couplingareas arranged at an intersection with the optical interference region(forming the reservoir layer), while the reservoir nodes 252 may beembodied as readout units.

The training process of the optical reservoir computing system 22 willchange the weights wi 253. However, the reservoir layer itself willremain fixed (other connections remain associated to fixed weights,which do not change during the training/learning process).

In operation, the output nodes 254 deliver an optical output signal,which can be converted into the electrical domain by suitableconverters, as known per se. The converted output signals may then befurther processed in the electrical domain by suitable hardware orsoftware processing means. In general, the adjustment of the weights 253may be done in software or hardware. E.g., a hardware control circuitwith additional control software running on it may receive the outputsignals of the output nodes 254 during the training process and mayadjust the weights of the optical weighting elements 253 by applyingelectrical control signals to the optical weighting elements 253. Theoptical weighting elements 253 may be, e.g., embodied as opticalattenuators or optical amplifiers. During the training process, certainstates of the reservoir system may be assessed. In particular, usingsome learning algorithms, the state of the output connections 254 afterthe weighting elements 254 might be invoked. Therefore, parts of theoptical signal might be split to a dedicated detector and fed to therespective learning algorithm during the training process.

An optical reservoir computing system 22 such as depicted in FIG. 4 mayadvantageously be operated according to the reservoir computingparadigm.

In embodiments, the optical-to-electrical conversion is carried out atthe optical output nodes 254. In variants, though, this conversion maybe carried out upstream the nodes 254, e.g., at the reservoir nodes 252.There, the output connections, the weighting elements 253, and theoutput nodes 254 may be embodied as electrical components. Note,however, that the optical reservoir itself and the reservoir nodes 252solely remain in the optical domain. In variants, the weighting elements253 and the output nodes 254 may be embodied in software.

In all cases, the output weights 253 can be trained, so as to form atrained (or controlled) layer formed by output nodes 254 andsubsequently infer results, during an inference stage.

FIG. 5 shows a schematic illustration of another photonic computingsystem according to embodiments.

The computing system 22 a comprises two feedback delay waveguides, whichare used to map temporal information contained in the optical inputsignal 54 into the optical interference pattern 510. The opticalinterference pattern has an optical power distribution representing theoptical power at respective locations of the optical interferencepattern.

The computing system 22 a comprises a plurality of readout units 252,embodying reservoir nodes, as discussed in respect of FIG. 4. Thereadout units 252 are arranged in an inner area of the opticalinterference region 510 as opposed to edges 241 (grey shading in FIG. 5)of the optical interference region 510. This inner area may for instancebe defined as the entire area of the optical interference region 510 butthe outer edges 241. The edges 241 could possibly be formed by a mirrorstructure, e.g. a Bragg reflector, or a metal coating on theinterference region 510. In variants, the edges 241 may correspond to atransition between the interference region 510 and a surrounding area(not shown), e.g., formed by a layer (e.g., SiO₂) having a differentrefractive index than the interference region 510 (e.g., Si).

The readout units 252 are configured to detect optical readout signalsRSi of the optical power distribution at readout positions RPi of theinner area of the optical interference region 510. The readout unit 252may for example be configured to detect optical intensities, opticalpowers, optical energies and/or information as to the optical phases.

The photonic computing system 22 a comprises two input delay waveguides221 and 222. The input delay waveguide 221 is meant to receive part ofan input signal IS, e.g., through a splitter or a coupler. The inputsignal IS then delayed by the input delay waveguide 221 and forwarded tothe interference region 510 as a delayed input signal IS_(d1) with afirst time delay d1. The delayed input signal IS_(d1) is furthermoreforwarded to the input delay waveguide 222, e.g., via a splitter orcoupler. The delayed input signal IS_(d1) is then further delayed by theinput delay waveguide 222 and forwarded to the interference region 510as a further delayed input signal IS_(d2) with a second time delay d2.Further combinations of feedback delay lines and input delay lines maybe contemplated, to achieve a desired temporal mapping.

In addition, the system 22 a may comprises nonlinear componentsimplemented as, e.g., thermo-optical elements, electro-optical elements,electrical feedback loops and/or optical cavities to map the temporalinformation of the optical input signal into the optical interferencepattern. Such nonlinear components provide a nonlinear dependence of theoptical interference pattern on the optical input signals.

For example, the optical computing system 22 a may possibly comprise oneor more nonlinear components 230, 242 for performing a nonlinear signaltransformation. The nonlinear components 242 may for instance bearranged in the interference region 510 (as assumed in FIG. 5). Suchnonlinear components 242 may for instance be provided as, e.g., aphotorefractive element, an optical amplifier or an attenuator.

In variants, nonlinear components may be arranged in an upstream inputwaveguide (not shown), the input delay waveguides 221, 222 and/or thefeedback delay waveguides. For example, optical cavities 230 may bearranged in the feedback delay waveguides 210 or the input delaywaveguides 221, 222, as schematically shown in FIG. 5. Such cavities maypossibly be configured to have a finite optical lifetime.

In other variants, the interference region 510 in the optical computingsystem 22 a may possibly comprise one or more scattering elements (e.g.,similar to elements 242) for scattering the optical wave and increasingthe complexity of the optical interreference pattern.

In other variants, the receiver 20 may comprise nonlinear elements thatdo not form part of the optical system 22 a itself.

2.2 Software Implementations of ANNs

As noted in Sect. 1 and 2.1, the ANNs may wholly or partly beimplemented in software. Thus, the present invention may be embodied asa system, a method, and/or a computer program product at any possibletechnical detail level of integration. The computer program product mayinclude a computer readable storage medium (or media) having computerreadable program instructions thereon for causing a processor to carryout aspects of the present invention.

The computer readable storage medium can be a tangible device that canretain and store instructions for use by an instruction executiondevice. The computer readable storage medium may be, for example, but isnot limited to, an electronic storage device, a magnetic storage device,an optical storage device, an electromagnetic storage device, asemiconductor storage device, or any suitable combination of theforegoing. A non-exhaustive list of more specific examples of thecomputer readable storage medium includes the following: a portablecomputer diskette, a hard disk, a random access memory (RAM), aread-only memory (ROM), an erasable programmable read-only memory (EPROMor Flash memory), a static random access memory (SRAM), a portablecompact disc read-only memory (CD-ROM), a digital versatile disk (DVD),a memory stick, a floppy disk, a mechanically encoded device such aspunch-cards or raised structures in a groove having instructionsrecorded thereon, and any suitable combination of the foregoing. Acomputer readable storage medium, as used herein, is not to be construedas being transitory signals per se, such as radio waves or other freelypropagating electromagnetic waves, electromagnetic waves propagatingthrough a waveguide or other transmission media (e.g., light pulsespassing through a fiber-optic cable), or electrical signals transmittedthrough a wire.

Computer readable program instructions described herein can bedownloaded to respective computing/processing devices from a computerreadable storage medium or to an external computer or external storagedevice via a network, for example, the Internet, a local area network, awide area network and/or a wireless network. The network may comprisecopper transmission cables, optical transmission fibers, wirelesstransmission, routers, firewalls, switches, gateway computers and/oredge servers. A network adapter card or network interface in eachcomputing/processing device receives computer readable programinstructions from the network and forwards the computer readable programinstructions for storage in a computer readable storage medium withinthe respective computing/processing device.

Computer readable program instructions for carrying out operations ofthe present invention may be assembler instructions,instruction-set-architecture (ISA) instructions, machine instructions,machine dependent instructions, microcode, firmware instructions,state-setting data, configuration data for integrated circuitry, oreither source code or object code written in any combination of one ormore programming languages, including an object oriented programminglanguage such as Smalltalk, C++, or the like, and procedural programminglanguages, such as the C programming language or similar programminglanguages. The computer readable program instructions may executeentirely on the user's computer, partly on the user's computer, as astand-alone software package, partly on the user's computer and partlyon a remote computer or entirely on the remote computer or server. Inthe latter scenario, the remote computer may be connected to the user'scomputer through any type of network, including a local area network(LAN) or a wide area network (WAN), or the connection may be made to anexternal computer (for example, through the Internet using an InternetService Provider). In some embodiments, electronic circuitry including,for example, programmable logic circuitry, field-programmable gatearrays (FPGA), or programmable logic arrays (PLA) may execute thecomputer readable program instructions by utilizing state information ofthe computer readable program instructions to personalize the electroniccircuitry, in order to perform aspects of the present invention.

Aspects of the present invention are described herein with reference toflowchart illustrations and/or block diagrams of methods, apparatus(systems), and computer program products according to embodiments of theinvention. It will be understood that each block of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer readable program instructions.

These computer readable program instructions may be provided to aprocessor of a general-purpose computer, special purpose computer, orother programmable data processing apparatus to produce a machine, suchthat the instructions, which execute via the processor of the computeror other programmable data processing apparatus, create means forimplementing the functions/acts specified in the flowchart and/or blockdiagram block or blocks. These computer readable program instructionsmay also be stored in a computer readable storage medium that can directa computer, a programmable data processing apparatus, and/or otherdevices to function in a particular manner, such that the computerreadable storage medium having instructions stored therein comprises anarticle of manufacture including instructions which implement aspects ofthe function/act specified in the flowchart and/or block diagram blockor blocks.

The computer readable program instructions may also be loaded onto acomputer, other programmable data processing apparatus, or other deviceto cause a series of operational steps to be performed on the computer,other programmable apparatus or other device to produce a computerimplemented process, such that the instructions which execute on thecomputer, other programmable apparatus, or other device implement thefunctions/acts specified in the flowchart and/or block diagram block orblocks.

The flowchart and block diagrams in the Figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods, and computer program products according to variousembodiments of the present invention. In this regard, each block in theflowchart or block diagrams may represent a module, segment, or portionof instructions, which comprises one or more executable instructions forimplementing the specified logical function(s). In some alternativeimplementations, the functions noted in the blocks may occur out of theorder noted in the Figures. For example, two blocks shown in successionmay, in fact, be executed substantially concurrently, or the blocks maysometimes be executed in the reverse order, depending upon thefunctionality involved. It will also be noted that each block of theblock diagrams and/or flowchart illustration, and combinations of blocksin the block diagrams and/or flowchart illustration, can be implementedby special purpose hardware-based systems that perform the specifiedfunctions or acts or carry out combinations of special purpose hardwareand computer instructions.

While the present invention has been described with reference to alimited number of embodiments, variants and the accompanying drawings,it will be understood by those skilled in the art that various changesmay be made and equivalents may be substituted without departing fromthe scope of the present invention. In particular, a feature(device-like or method-like) recited in a given embodiment, variant orshown in a drawing may be combined with or replace another feature inanother embodiment, variant or drawing, without departing from the scopeof the present invention. Various combinations of the features describedin respect of any of the above embodiments or variants may accordinglybe contemplated, that remain within the scope of the appended claims. Inaddition, many minor modifications may be made to adapt a particularsituation or material to the teachings of the present invention withoutdeparting from its scope. Therefore, it is intended that the presentinvention not be limited to the particular embodiments disclosed, butthat the present invention will include all embodiments falling withinthe scope of the appended claims. In addition, many other variants thanexplicitly touched above can be contemplated.

What is claimed is:
 1. A method of demodulating a modulated signal, themethod comprising: receiving a modulated signal, wherein the modulatedsignal is a signal modulated according to a modulation function varyingfaster than the signal, the modulation function being a function of thesignal; and demodulating the modulated signal received with anartificial neural network (ANN) system, the ANN system trained toidentify bit values from signal patterns as caused by the modulationfunction, by identifying bit values from patterns of the modulatedsignal received, wherein said signal encodes, prior to modulating it, an-ary code, with n larger than or equal to two, and the modulated signalencodes, after modulating it, a m-ary code, with m strictly larger thann.
 2. The method according to claim 1, wherein the method furthercomprises, prior to receiving the modulated signal: modulating thesignal according to said modulation function to obtain said modulatedsignal; and transmitting the modulated signal obtained, for it to bereceived and subsequently demodulated by the ANN system.
 3. The methodaccording to claim 2, wherein, the signal is a digital signal; and atmodulating, the signal is modulated over each time period correspondingto each of the discrete values captured by the digital signal,respectively, to obtain the modulated signal.
 4. The method according toclaim 3, wherein modulating the digital signal comprises: for each ofsaid discrete values, modulating said digital signal according to saidmodulation function based on two or more discrete values of the digitalsignal, the discrete values including said each of the discrete values,as well as one or more previous discrete values of the digital signal.5. The method according to claim 3, wherein modulating the digitalsignal comprises streaming the digital signal to a modulator, for it tomodulate the signal streamed on the fly, and transmitting comprisesstreaming the modulated signal to the ANN system for it to demodulatethe streamed signal it receives on the fly.
 6. The method according toclaim 2, wherein at transmitting, the modulated signal is opticallytransmitted.
 7. The method according to claim 6, wherein the modulatedsignal received is an optical signal and the ANN system forms part of aphotonic computing system, configured as a reservoir computing system,and the method further comprises coupling the modulated signal receivedinto the ANN system for the ANN system to demodulate the coupled signalby identifying bit values from patterns of the coupled signal.
 8. Themethod according to claim 7, wherein the signal is modulated with anelectro-optic modulator, prior to being optically transmitted, for thetransmitted signal to be received and subsequently demodulated by thephotonic computing system.
 9. The method according to claim 8, whereinmodulating the signal comprises modulating an amplitude and/or a phaseof an electromagnetic field carrying the signal.
 10. The methodaccording to claim 2, wherein modulating comprises modulating two ormore input signals according to the modulation function, so as to obtainone or more modulated signals, each varying faster than the inputsignals, the modulation function being a function of the input signals,such that one or more modulated signals are subsequently received; andthe one or more modulated signals received are demodulated with the ANNsystem, by identifying bit values from patterns of the one or moremodulated signals received.
 11. The method according to claim 2, whereinthe method further comprises after demodulating the modulated signal,adapting the modulation function based on feedback obtained from thedemodulated signal, so as to adapt a property of a next modulatedsignal, and modulating a subsequent signal based on the adaptedmodulation function.
 12. The method according to claim 1, wherein themethod further comprises converting the modulated signal received into adiscrete signal, for the ANN system to demodulate the converted signalby identifying bit values from patterns of values in the convertedsignal.
 13. The method according to claim 1, wherein the ANN system isimplemented as a trainable hardware device, the method furthercomprises, prior to demodulating the modulated signal received, mappingtemporal information captured by the modulated signal received onto oneor more input nodes of an input layer of the ANN system, wherein the ANNsystem further comprises an output layer of one or more output nodes,wherein the input nodes of the input layer are connected to output nodesof the output layer via connections, wherein at least some of theseconnections are associated to adjustable weight elements, andidentifying said bit values comprises reading signals from said outputnodes.
 14. The method according to claim 13, wherein said modulatedsignal is received as an optical input signal, and the ANN system isimplemented as part of a photonic computing system configured as areservoir computing system, whereby mapping said temporal informationcomprises coupling said optical input signal onto an input node of thereservoir computing system, wherein the input node is connected to oneor more optical output nodes of the output layer via optical reservoirnodes of a reservoir layer of the reservoir computing system, each ofsaid optical output nodes is connected by one or more of the opticalreservoir nodes via respective connections, and adjustable weightelements are respectively associated to said respective connections. 15.The method according to claim 1, wherein the method further comprisestraining the ANN system, for it to identify bit values from signalpatterns as caused by the modulation function.
 16. A demodulator fordemodulating a signal, the demodulator comprising: an input unitconfigured to receive a modulated signal that is a signal modulatedaccording to a modulation function varying faster than the signal, themodulation function being a function of the signal; and an artificialneural network (ANN) system, connected to the input unit for the inputunit to couple the received signal into the ANN system, in operation,wherein the ANN system is trained to identify bit values from signalpatterns as caused by the modulation function and configured todemodulate the modulated signal coupled into it by identifying bitvalues from patterns of the modulated signal received, wherein the ANNsystem is implemented as a trainable hardware device in the demodulator,whereby the ANN system comprises an input layer of one or more inputnodes and an output layer of one or more output nodes, wherein the inputnodes are connected to the output nodes via connections and at leastsome of these connections are associated to adjustable weight elements,and wherein the ANN system is configured to identify bit values byreading signals from said output nodes.
 17. The demodulator according toclaim 16, wherein the ANN system is a photonic computing systemconfigured as a reservoir computing system, the latter adapted todemodulate a modulated optical signal by identifying bit values frompatterns of the modulated optical signal received by the input unit andcoupled into the ANN system, in operation.
 18. The demodulator accordingto claim 16, wherein the ANN system is implemented as a photoniccomputing system configured as a reservoir computing system, whichcomprises a single input node connected to one or more optical outputnodes of the output layer via optical reservoir nodes of a reservoirlayer thereof, each of said optical output nodes is connected by one ormore of the optical reservoir nodes via respective connections,adjustable weight elements are respectively associated to saidrespective connections, and the input unit is configured to receive saidmodulated signal as an optical input signal and couple the latter intothe single input node.
 19. A modulation system for modulating anddemodulating a signal, the system comprising: a modulator configured tomodulate a signal according to a modulation function to obtain amodulated signal, wherein the modulation function is a function of thesignal, which vary faster than the signal, a transmission unitoperatively connected to the modulator to transmit modulated signalobtained by the latter, a demodulator that comprises: an input unitconfigured to receive a modulated signal transmitted by the transmissionunit, in operation; and an artificial neural network (ANN) system,connected to the input unit for the input unit to couple the receivedsignal into the ANN system, in operation, wherein the ANN system istrained to identify bit values from signal patterns as caused by themodulation function and thereby configured to demodulate the modulatedsignal coupled into it by identifying bit values from patterns of themodulated signal it receives, in operation, wherein the signal is adigital signal and the modulator is configured to modulate the digitalsignal over each time period corresponding to each of the discretevalues captured by the digital signal, respectively, to obtain themodulated signal.
 20. The modulation system according to claim 19,wherein the modulator is further configured to modulate, for each ofsaid discrete values, said digital signal according to said modulationfunction, based on two or more discrete values of the digital signal,the discrete values including said each of said discrete values, as wellas one or more previous discrete values of the digital signal.
 21. Themodulation system according to claim 19, wherein the modulator isadapted to modulate a streamed signal on the fly, and the ANN system isconfigured to demodulate a modulated signal it receives on the fly. 22.The modulation system according to claim 19, wherein each of themodulator and the ANN system is a photonic computing system.